According to government data, the probability that an adult was never in a museum is 15%. In a randomsurvey of 10 adults, what is the probability that two or fewer were never in a museum?
A) 0.820
B) 0.002
C) 0.800
D) 0.200

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 10 (number of trials), p = 0.15 (probability of success, which in this context is an adult never having been in a museum), and we are looking for the probability of x ≤ 2 successes (two or fewer adults never having been in a museum). The formula for binomial probability is P(X = x) = (nCx) * p^x * (1-p)^(n-x), where nCx is the combination of n items taken x at a time. To find the probability of two or fewer, we calculate P(X = 0), P(X = 1), and P(X = 2) and sum these probabilities. The exact calculations can be tedious without a calculator but generally result in a sum that is closest to the option A) 0.820, indicating a high likelihood that in a random survey of 10 adults, two or fewer will have never been in a museum.

According to Government Data, the Probability That an Adult Was